Abstract: Suppose is a Dedekind domain of characteristic 2 and is an inner product space, i.e. is a finitely generated projective module supplied with a nonsingular symmetric bilinear form . It is shown that is determined up to isometry by the extension of to , where is the quotient field of , and the value module of all for in . In particular, a hyperbolic space is completely determined by the rank of the finitely generated projective module . As consequences, genera coincide with isometry classes, and if and are isometric nonsingular submodules of such that , then and are isometric. Also, given an inner product space and a submodule of , a necessary and sufficient condition is given for the existence of a inner product space such that and .